// Numbas version: exam_results_page_options
{"name": "Maria's copy of Choose the probability of getting certain scores on a die", "extensions": [], "custom_part_types": [], "resources": [["question-resources/dice.svg", "/srv/numbas/media/question-resources/dice.svg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>First part&nbsp;asks for the probability of rolling an even number. Second part asks for the probability of not rolling either of two given numbers.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"css": "", "js": ""}, "advice": "<p>For equally likely outcomes, you can calculate the probability of a particular event occurring&nbsp;by using the formula</p>\n<p>$\\text{Probability of an event} = \\displaystyle\\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}}$.</p>\n<p>Rolling a fair six-sided die has six possible outcomes, each of which is equally likely.</p>\n<p>Let's say we want to find the probability&nbsp;of&nbsp;rolling a $2$. There is&nbsp;only one outcome which involves a $2$ being rolled, so the number of favourable outcomes is $1$.</p>\n<p>Hence using the above formula,</p>\n<p>\\begin{align}<br/>P(\\text{rolling a $2$}) &amp;= \\displaystyle\\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}}\\\\<br/>&amp;= \\displaystyle\\frac{1}{6}<br/>\\end{align}</p>\n<h4>a)</h4>\n<p>There are three possible outcomes where we roll an even number on the die:</p>\n<ul>\n<li>we roll a $2$;</li>\n<li>we roll a $4$;</li>\n<li>we roll a $6$.</li>\n</ul>\n<p>Using the formula for probability&nbsp;for equally likely outcomes, this means that</p>\n<p>\\[<br/>P(\\text{rolling an even number}) = \\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}}= \\frac{3}{6} = \\frac{1}{2}<br/>\\]</p>\n<h4>b)<em>&nbsp;</em></h4>\n<p>To find the probability of not rolling a $\\var{die1}$ or a $\\var{die2}$, we use the same formula again.</p>\n<p>The total number of outcomes is still $6$.</p>\n<p>Here, we have four possible outcomes which don't involve rolling a $\\var{die1}$ or a $\\var{die2}$, i.e. when we roll any of the other numbers on the die.</p>\n<p>Using the formula,</p>\n<p>\\[<br/>P(\\text{not rolling a $\\var{die1}$ or a $\\var{die2}$}) = \\frac{\\text{number of favourable outcomes}}{\\text{total number of outcomes}} = \\frac{4}{6} = \\frac{2}{3}<br/>\\]</p>\n<h4></h4>", "functions": {}, "extensions": [], "rulesets": {}, "statement": "<p>You're going to roll a fair six-sided die.</p>", "variablesTest": {"maxRuns": "100", "condition": ""}, "name": "Maria's copy of Choose the probability of getting certain scores on a die", "variables": {"red": {"description": "<p>number of red balls in part c</p>", "name": "red", "definition": "random(15,19)", "group": "Ungrouped variables", "templateType": "anything"}, "die1": {"description": "<p>Not included number for a) ii)</p>", "name": "die1", "definition": "random(1..3)", "group": "Ungrouped variables", "templateType": "anything"}, "die2": {"description": "<p>Not included number for a) ii)</p>", "name": "die2", "definition": "random(4..6)", "group": "Ungrouped variables", "templateType": "anything"}}, "ungrouped_variables": ["red", "die1", "die2"], "parts": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "maxMarks": 0, "shuffleChoices": false, "showFeedbackIcon": true, "displayType": "radiogroup", "choices": ["<p>$1$</p>", "<p>$\\displaystyle\\frac{2}{3}$</p>", "<p>$\\displaystyle\\frac{1}{2}$</p>", "<p>$\\displaystyle\\frac{1}{3}$</p>"], "distractors": ["", "", "", ""], "scripts": {}, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0, "displayColumns": 0, "matrix": [0, 0, "1", 0], "variableReplacements": []}], "showFeedbackIcon": true, "prompt": "<p>What is the probability of rolling an even number?</p>\n<p>[[0]]</p>", "variableReplacements": []}, {"variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "gaps": [{"variableReplacementStrategy": "originalfirst", "marks": 0, "maxMarks": 0, "shuffleChoices": false, "showFeedbackIcon": true, "displayType": "radiogroup", "choices": ["<p>$0$</p>", "<p>$\\displaystyle\\frac{2}{3}$</p>", "<p>$\\displaystyle\\frac{1}{3}$</p>", "<p>$\\displaystyle\\frac{1}{4}$</p>"], "distractors": ["", "", "", ""], "scripts": {}, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0, "displayColumns": 0, "matrix": ["0", "1", 0, 0], "variableReplacements": []}], "showFeedbackIcon": true, "prompt": "<p>What is the probability of&nbsp;not rolling a $\\var{die1}$ or $\\var{die2}$?</p>\n<p>[[0]]</p>", "variableReplacements": []}], "tags": ["taxonomy"], "variable_groups": [], "type": "question", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Maria Aneiros", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3388/"}]}